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1

2 1. : ( ): : 1

3

4

5 ( )

6 / minimum solar nebula model

7 ( )

8

9

10

11 ( )

12 ( ) SDSS

13 : d 2 r i dt 2 ÿ j i Gm jr ij r 3 ij

14 : : :

15 =

16 Newton

17 3 0.1%

18 19

19 20 20

20 2

21 ( )

22 3 3 (2 )

23 3 3

24 3 2,3

25 20 Figure-8 Solution

26 Figure-8 solution 3 (0.005% )

27

28 d 2 x fpxq (1) dt2 xp0q x 0, dx dt t 0 vp0q v 0 (2)

29 1 dx{dt fpxq xpt ` tq xptq ` tfpxptqq 1

30 1987 2

31 e 2 8.5

32 45 2

33 2009 Nature :

34 Laskar and Gastineau 2009 ( 0.38mm)

35

36

37

38 ( )

39 ( ) )

40 X X

41

42 1

43

44

45 Ill-posed problem??

46

47 :

48

49 fpx, vq : 6 fpx, vqdxdv dxdv

50 Bf Bt ` v f Φ Bf Bv 0, (3) Φ 2 ϕ 4πGρ. (4) G

51 ρ ρ m ż dvf, (5)

52

53 .

54

55 ( ) : ( )

56 ( ) : ( ) ( ) ( )

57 Bv Bt Bρ ` pρvq 0 Bt (6) ` pv qv 1 p Φ ρ (7) 2 Φ 4πGρ (8)

58 ρ: t: v: p: Φ: G:

59 ρ, p, v, Φ ρ ρ 0 ` ρ 1 0 1

60 Bρ 1 Bt ` pρ 0v 1 q ` pρ 1 v 0 q 0 (9) Bv 1 Bt `pv 0 qv 1`pv 1 qv 0 ρ 1 p 1 0 p 1 Φ ρ 2 1 (10) 0 ρ 0 v s 2 Φ 1 4πGρ 1 (11) ˆdp p 1 ρ 1 v 2 s dρ ρ 1 (12) 0

61 0 Bρ 1 Bt ` ρ 1 pρ 0 v 1 q 0 (13) Bv 1 Bt 1 ρ 0 p 1 Φ 1 (14) 2 ρ 1 B 2 ρ 1 Bt 2 v2 s 2 ρ 1 4πGρ 0 ρ 1 0 (15)

62 2

63 ( ) ρ 1 Ce ipk x ωtq (16) ω 2 v 2 s k2 4πGρ 0 (17) k 2 J 4πGρ 0 v 2 s (18)

64 k ą k J ω k k J ω 0 k ă k J ω (16)

65 1{k J

66 k J : λ J λ J c π Gρ 0 v s (19) : M J v 2 s GM J {λ J M J ( λ J )

67 0 : ( )

68 1996

69

70 M82

71 X NASA Chandra X

72 Ñ Ñ

73 2 2

74 Ó

75 dp dm M 4πr4, (20) dr dm 1 4πr 2 ρ, (21) Mprq r p ρ 1

76 ( ) dp dr ρm r 2 (22) p ρt (23)

77 (3) ρ9r 2 ( ) ( ) r Ñ 8

78 : (D ) : D ( ) 1

79 r, m, t G 1 1{r 1{m r{m 2 ( ) t{m ( )

80

81 D D

82

83

84 Ñ Ñ Ñ Ñ Ñ

85

86 Bf Bt Apfpxqq (24) A f 2 f f 0 pxq Apf 0 pxqq 0 f f 0 ` df df

87 (1) df df

88 (2) : df f 0 df : Bdf Bt Bpdfpxqq (25) Bpαdf 1 pxq ` βdf 2 pxqq αbpdf 1 pxqq ` βbpdf 2 pxqq (26)

89 (3) df 1 df 1 df 1, df 2 df 1 ` df 2

90 λ λdf Bpdfq (27) df e λt df 0

91 λ

92 f 0 f 0 df

93 df

94 , D 1.05 λ:

95 (2), D 10

96 (3), D 100

97 , D 709

98 , D 1000

99 gravothermal instavility V. Antnov (1961) : Hachisu & Sugimoto (1978)

100 Hachisu et al. (1978) : Cohn (1980):

101

102 3

103

104

105 ( )

106

107 : %

108 :

109 1 : (6 ) ( )

110 k ω v s Σ κ ω 2 κ 2 2πGΣ k ` v 2 s k2 (28) :

111 R ΦpRq R Φ eff Φ ` L2 z 2R 2 (29) d 2 R dt 2 dφ eff dr (30) R R 0 ` x d 2 x dt 2 κ2 x (31)

112 κ 2 d2 Φ dr 2 ` 3 R 0 dφ dr (32) ( R R 0 )

113 κ Ω Ω 2 1 dφ R dr κ 2 R 0 dω 2 (33) dr ` 4Ω2 (34) κ Ω 2Ω Ω ă κ ă 2Ω (35)

114 (28) ω 2 v 2 s k2 4πGρ 0 (36) ω 2 κ 2 2πGΣ k ` v 2 s k2 (37)

115 v 2 s k2 4πGρ 0 2πGΣ k 3 = 2 κ 2

116 0 v s 0 0 k crit κ2 2πGΣ ; λ crit 2π k crit 4π2 GΣ κ 2 (38) ( ) : 2

117 k ω κ 2 2πGΣ k ` v 2 s k2 ě 0 (39) v s κ πgσ ą 1 (40) Q v sκ πgσ (41) Toomre Q

118 ( ) Q σ Rκ 3.36GΣ ą 1 (42) σ R (π 3.36)

119 : R

120 3 λ crit λ crit 4π2 GΣ κ 2 (43) 1 λ crit Σ (κ 1 ) Σ λ crit

121 1 0.1 λ crit Q

122 tight winding

123 tight-winding tight winding : ( ) = m pω mωq 2 κ 2 2πGΣ k ` v 2 s k2 (44)

124 tight-winding m 0 mω tight-winding Ω

125 グローバルなスパイラルモード 実際の銀河では 全く tight-winding も局所近似 も成り立たないような大き なスケールでのスパイラル 構造が見つかっている 中間赤外で見える低温のガ スは複雑な構造をもつ 大きなスケールでのスパイ M101 銀河 スピッツアー衛星 ラルアームがあるように見 での赤外線画像 える 多くの銀河についてそういう構造があるように見える

126 ( )

127 ( ) 1. ( Lin-Shu ) 2.

128

129 ( )

130 Q 1 Q

131 Q 90 (Fujii et al, 2011) Q

132 Swing Amplification swing amplification

133 Swing Amplification(2) leading arm ( ) trailing trailing leading trailing

134 Swing Amplification(3) leading arm N

135 Q 1970

136 :

137 Katz and Gunn Cray YMP : 1000

138 Saitoh et al GRAPE-5 1 (!) animation 1 : 1

139 :

140 1 : 4-5 :

141 1-2

142 Saitoh et al

143 Star formation with SPH Large scale structure formation with AMR

144 animation (Baba et al 2009) 1 2

145 SPH Cray XT4 ASURA 10pc (Ð 500pc) 10K (Ð 10 4 K ) 3000M d (Ð 10 5 M d )

146 高分解能モデルと観測

147 低分解能モデルと観測

148

149 2006: Xu et al, Science 311, 54 Nov 2008: Burst of results from VLBA Several data from VERA (Compiled by Dr. Asaki)

150 ( 30km/s)

151

152

153

154 ( ) ( )

155 星のスパイラルの運動 星の運動の円運動からのずれ スパイラルアームは実体 密度波では ない 古い星の平均の円運動からのずれ も結構大きい キロパーセクスケールの構造があ る

156 +

157 : -

158 : -

159 Svensmark 2007 :

160 1.4 ( ) : (???)

161

162 ( )

163 ( )

164 : :

165

166 : ( ) : :

167 : 6-10

168 (Fujii et al. 2010) animation a1 animation a2 animation b1 Stable against radial mode (a1, a2) Spiral arms form They seem to be maintained for very long time

169 : ( )

( )

( ) 1. 2. 3. 4. 5. ( ) () http://www-astro.physics.ox.ac.uk/~wjs/apm_grey.gif http://antwrp.gsfc.nasa.gov/apod/ap950917.html ( ) SDSS : d 2 r i dt 2 = Gm jr ij j i rij 3 = Newton 3 0.1% 19 20 20 2 ( ) 3 3

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